MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

First Derivative Test for Local Maximum

Let Px=a0+a1x...

Question

Let $P (x) = a_{0} + a_{1} x^{2} + a_{2} x^{4} + . . . . . . + a_{n} x^{2 n}$ be a polynomial in a variable x with $0 < a_{0} < a_{1} < a_{2} < a_{3} . . . . . . . < a_{n}$ . The function P(x) has

A

neither a maximum nor a minimum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

only one maximum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

only one minimum

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

only one maximum and only one minimum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

E

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C only one minimum
$We have, P (x) = a_{0} + a_{1} x^{2} + a_{2} x^{4} + . . . . . . + a_{n} x^{2 n} ∴ P' (x) = 2 a_{1} x + 4 a_{2} x^{3} + . . . . . . + 2 n a_{n} x^{2 n - 1} \Rightarrow P' (x) = x (2 a_{1} + 4 a_{2} x^{2} + . . . . . . + 2 n a_{n} x^{2 n - 2}) Clearly, P' (x) > 0 for x > 0 and P' (x) < 0 for x < 0 . Thus, P (x) increases for all x > 0 and decreases for all x < 0 . Also, P (x) cannnot be less than 0 as all the coefficients are positive and powers of variable x are all even . ∴ P' (x) has x = 0 as the point of minima .$

Suggest Corrections

thumbs-up

0

Similar questions

P (x) = a_{0} + a_{1} x^{2} + a_{2} x^{4} + . . . + a_{n} x^{2 n}

be a polynomial in a real variable x with

0 < a_{0} < a_{1} < a_{2} < . . . < a_{n} .

The function P(x) has

P (x) = a_{0} + a_{1} x^{2} + a_{2} x^{4} + . . . + a_{n} x^{2 n}

be a polynomial in a real variable x with

0 < a_{1} < a_{2} . . . < a_{n}

P (x) = a_{0} + a_{1} x^{2} + a_{2} x^{4} + . . . . . . + a_{n} x^{2 n}

be a polynomial in a variable x with

0 < a_{0} < a_{1} < a_{2} < a_{3} . . . . . . . < a_{n}

. The function P(x) has

P (x) = a_{0} + a_{1} x^{2} + a_{2} s^{4} + . . . . . . . . + a_{n} x^{2 n}

be a polynomial in a real variable x with

0 < a_{0} < a_{1} < a_{2} < . . . . < a_{n^{'}}

The function P(x) has

P (x) = a_{0} + a_{1} x^{2} + a_{2} x^{4} + a_{3} x^{6} + . . . + a_{n} x^{2 n}

be a polynomial in a real variable

x

0 < a_{0} < a_{1} < a_{2} . . . < a_{n}

P (x)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

First Derivative Test for Local Maximum

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon